I have no opinion or interest in the size of YC batches. But just wanted to point out that this:

>The primary reason we got more applications is that over 15K companies participated in our startupschool.org program

Comes across as insincere and hurts the credibility of the rest of your response. It’s just not plausible that a brief online course made a major difference in the number of YC worthy companies out there. Just go with the real reason. (Eg. We have more money and partners, we happened to get a strong application batch, etc.)